Club steak is a name for a bone-in strip steak. It's a roughly triangular steak with an L-shaped bone. The club steak is similar to a T-bone steak, but it's taken from the front part of the short loin, the part nearest the rib, so it doesn't have any of the tenderloin.
Alternately, club steaks can come from short loins where the tenderloin has been removed, in which case it can come from the anterior (front) or posterior (rear) of the short loin.
All else being equal, steaks from the anterior of the short loin are more tender than ones from the posterior.
You can tell by looking at the steak in the photo above that it's from the posterior end of the short loin. The way to know that is by the oblong section of meat you can see on the left side of the steak. That is the gluteus, or sirloin muscle, and it's only present in maybe the last one or two steaks before the short loin becomes the sirloin.
You might hear a steak like the one in the picture referred to as a "vein steak" because of the white vein of connective tissue between the gluteus and the main muscle of the strip steak, called the multifidus. The multifidus is much more tender than the gluteus. But overall, any steak from the short loin is going to be pretty good.
As for the bone in a club steak, it's the same bone that makes the T in a T-bone, but with one arm of the T missing, so it makes an L rather than a T.
When fabricating a beef short loin, the butcher can either leave in the tenderloin and make T-bone and porterhouse steaks, or remove the tenderloin and make club steaks or strip steaks.
The naming of steaks is one of those practices where the origins are hazy and most stories are unreliable.
For instance, some people say that club steaks are named because they were traditionally served at high-end establishments such as country clubs.
Others claim that the L-shaped bone looks like something you might club someone with. Knowing what I know about the people who work in kitchens, I tend to give more credence to second story than the first. But no one knows for sure.
You might also hear the club steak called a shell steak. But whatever it's called, it's a strip steak with an L-shaped bone. is it possible to order a club steak and get a strip steak with just a straight piece of bone — or no bone at all? Absolutely. But that's because the taxonomy of steaks might as well have been organized by cats.
Speaking of obscure naming origins, "Delmonico" is another name that's been applied to virtually every steak under the sun — including the club steak. You can read more about that story here.